The Value of Buffers

The water system that my brother and his team put in in January was still not working when we left in June. We had a problem with a part, and pressure issues (we were trying to treat water too far below the storage facility -- we needed to raise the treatment system 10 feet into the air).

In the meantime, however, one change we made in the water system on campus had a huge impact: we added a 600 gallon tank into the system, as extra storage. This relatively large quantity of water made a huge difference in our "water security". This had not been an objective of the project, but was rather another unintended consequence (and a very positive one!).

"Water infrastructure is critical in reducing unpredictability and mitigating risk. Globally, the inequalities in access to infrastructure are very large. They are reflected in simple indicators: for water storage capacity: the United States stores about 6,000 cubic metres of water per person; Ethiopia, 43. Even rich countries are exposed to water-related disruption, however, as evidenced by the impact of Hurricane Katrina on New Orleans. But the risks weigh most heavily on poor countries." (Human Development Report 2006, p. 15)

We doubled storage capacity on campus from 600 gallons to 1200 gallons, and the impact was remarkable.

Activity:

Objective: To demonstrate the value of a buffer in the water system at Ivy's house (and more generally, of course!). This is a game, that is best played with several players (one assuming each role, given by the variables and parameters listed in the table below).

Background: When we arrived on campus, there were two tanks on campus that provided water to the house:

a 400-gallon tank (Upper tank), fed by an electric pump in a well; and
a 200-gallon tank (Lower tank) near the house, which was fed by the first tank.

There were a couple of problems that tended to make the situation worse than expected:

The tank below was filled by turning on a valve. The people in the house knew that the lower tank was full when it overflowed (and hence the water that overflowed was wasted). Worse yet, occasionally no one noticed that the water was overflowing, so the upper tank could be drained completely to leave the lower tank full (and the rest of the water wasted).
Occasionally kids -- rascals -- would turn off the pump to the Upper tank. So a day might go by with no input to the Upper tank.
Sometimes the solar panels that powered the pump wouldn't produce enough power to run the pump:
- The panels could get dirty the sun wouldn't penetrate the dirty film; and
- sometimes the weather was overcast and the panels wouldn't receive enough power through the clouds.

The worst case scenario is that we run out of water at the house. That represents a serious failure, and we will monitor that to see if the buffer helps to reduce that.

Model:

Variable/Parameter Name	Description
U_i	quantity of water in the Upper tank at time i
B_i	quantity of water in the Buffer tank at time i
L_i	quantity of water in the Lower tank at time i
D_i	household water Demand at time i
CU_i	Chance at time i that we empty the Upper tank by accident
CP_i	Chance that the pump is turned off at time i

Use this data table to play

Each person will play one role. And each variable or parameter uses a different set of data over the course of the day. The role and choices of each role are explained below.

Time i U_i B_i L_i D_i CU_i CP_i Failure?

Questions/Comments/Problems:

Notes:

Buffers are not always the answer, of course: "Just in Time" logistics argue against "buffers" (that is, inventory), because it costs money to keep the inventory around (e.g. in a warehouse).

Website maintained by Andy Long. Comments appreciated.